You don't need special skills to do this. After meeting Ashura, Jack was also stopped bleeding and bandaged by his subordinates.
Let's make this simple. Find the page that says Jacks mean used Ussop's Toad oil and not actual medicine to treat jack. In fact find the page that says NO ONE EVER USES ACTUAL MEDICINE to treat anybody and they just add bandages to treat every single thing, including Chopper also doesn't have actual medical expertise and just uses bandages.
You seem to be caught between the belief that Bandages alone are actually considered medical treatment and all along everyone is one piece doesn't have actual medicine and everyone including chopper uses loose bandages for every sort of treatment and you also don't want to believe that Oda specifies that Hiyori is using bad medicine to show that she actually doesn't know what she's doing and that she actually isn't applying any meaningful medical assistance
So it's fine, just find the page where Jacks men are proven to be as incompetent as Hiyori by using Ussop's toad oil or find the page where Chopper says that all it takes is plain bandages to treat wounds.
Also why are you posting fan translations when I posted the official translation MULTIPLE TIMES already?